a,cmr \(\left(\sqrt{a}+\dfrac{b-\sqrt{ab}}{\sqrt{a}+\sqrt{b}}\right):\left(\dfrac{a}{\sqrt{ab}+b}+\dfrac{b}{\sqrt{ab}-a}-\dfrac{a+b}{\sqrt{ab}}\right)=\sqrt{b}-\sqrt{a}\)
b, A=\((\dfrac{a-\sqrt{a}}{\sqrt{a}-1}-\dfrac{\sqrt{a}+1}{a+\sqrt{a}}):\dfrac{\sqrt{a}+1}{a}\)
1.tìm đk của A để A có ngĩa
2.rút gọn A
3.tìm GTNN của A
b:
1: ĐKXĐ: a>0; a<>1
2: \(A=\left(\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}-\dfrac{\sqrt{a}+1}{\sqrt{a}\left(\sqrt{a}+1\right)}\right)\cdot\dfrac{a}{\sqrt{a}+1}\)
\(=\left(\sqrt{a}-\dfrac{1}{\sqrt{a}}\right)\cdot\dfrac{a}{\sqrt{a}+1}\)
\(=\dfrac{a-1}{\sqrt{a}}\cdot\dfrac{a}{\sqrt{a}+1}=\sqrt{a}\left(\sqrt{a}-1\right)\)
3: \(A=a-\sqrt{a}+\dfrac{1}{4}-\dfrac{1}{4}=\left(\sqrt{a}-\dfrac{1}{2}\right)^2-\dfrac{1}{4}\ge-\dfrac{1}{4}\)
Dấu '=' xảy ra khi a=1/4
